Bifilar Pendulum: Can't justify/create a hypothesis + analyze results

[lavenders2]

Bifilar Pendulum: Need help with formulas now...

Homework Statement

So I have an assignment where I have to determine the relationships between the period of a Bifilar Pendulum. I performed an experiment where the angle was set to 20 degrees, the ruler tied to the strings is twisted, and then it is let go and after 3 periods, the timer is stopped. The independent variables are the length of the strings and the distance between the strings.

The above photo should help you understand what a bifilar pendulum looks like. The experiment my group performed was very similar to the set up shown in the picture.

We also had to create a hypothesis, justify it and then justify the results. I would really like to do well for this assignment, but the problem is I can't create a good hypothesis because the information on the internet seems limited. The reason I didn't create a hypothesis before the actual experiment is because there wasn't enough theory found to create one.

Homework Equations

This is what I am trying to find. Justifying the hypothesis is really as easy as saying "an expert on the matter said this would happen." So what if he was wrong/the experiment says he is wrong? At least I have my experiment results to compare it to, and see whether similar results were obtained, and then I can restate a hypothesis. However, I would like it if someone could help me link my hypothesis to physics theories (so why is the period proportional to the inverse of the length?) so I can do the best I can.

The Attempt at a Solution

So far I have my results, and found the relationships between the period with my independent variables. T=k x 1/d where T is period, k is the constant and d is the distance between the strings. In addition, T=o x √l where o is the second constant and l is the length of the strings vertically. However, when one of the 2 constants is found (because the constants are different for each variable), they are used again in the same formula with the same variables, and the answer comes out wrong. Is this because of human error? I'm fairly sure the constant is equal to the gradient of a graph where the two variables (time and 1/d) are plotted. Is this correct?

So to wrap it all up, can someone help me create a justifiable hypothesis (that is not based on my results obviously) and help me analyze me results? You would help me a lot!

 

[lavenders2]

Can nobody help me?
I was looking around, and came across this site:
http://www.egglescliffe.org.uk/physics/gravitation/bifilar/bif.html
I am using that to create a hypothesis, and have created one. Now I need to justify my hypothesis. However, I have gotten stuck at one point...

"Therefore the restoring Couple, CR, which acts towards the equilibrium position so is negative, is given by:

CR = (-Mgθd²)/4y


Applying Newton’s Second Law for the rotational motion of the rod, which is of constant mass:

(Id2θ)/dt2= (-Mgθd²)/4y

∴(d2θ)/dt2= (-Mgθd²)/4Iy"

Could someone read over the site and explain how this person came to this conclusion? I don't understand how he got the CR, or how he got the two formulas below that.

 

[SammyS]

Can nobody help me?
I was looking around, and came across this site:
http://www.egglescliffe.org.uk/physics/gravitation/bifilar/bif.html
I am using that to create a hypothesis, and have created one. Now I need to justify my hypothesis. However, I have gotten stuck at one point...

"Therefore the restoring Couple, CR, which acts towards the equilibrium position so is negative, is given by:

CR = (-Mgθd²)/4y

Applying Newton’s Second Law for the rotational motion of the rod, which is of constant mass:

(Id2θ)/dt2= (-Mgθd²)/4y

∴(d2θ)/dt2= (-Mgθd²)/4Iy"

Could someone read over the site and explain how this person came to this conclusion? I don't understand how he got the CR, or how he got the two formulas below that.

Hello lavenders2. Welcome to PF .

The following link may help: http://level1.physics.dur.ac.uk/projects/script/bifilar.pdf

I'll try to look at the link you gave to see if I can explain how Faysal Riaz got that result.

 

[lavenders2]

Hello lavenders2. Welcome to PF .

The following link may help: http://level1.physics.dur.ac.uk/projects/script/bifilar.pdf

I'll try to look at the link you gave to see if I can explain how Faysal Riaz got that result.

Thanks!
The link you gave wasn't too helpful, but it did have a nice diagram.
On the bright side, I may have worked out what Faysal Riaz has done.

The CR is the restoring couple. That means it has the opposite direction to the TR. Would the CR, by any chance, have anything to do with this?
T=F x d
Where T is the torque (in this case the resultant moment of a couple), F is one of the forces (the restoring forces) and d is the perpendicular distance between the forces (equal to the string separation, or in the formula the Faysal Riaz used, d) Because the CR is negative, we have:
(-Mgθd)/4y x d = (-Mgθd²)/4y

For the next part, we have:
F_net = m x (d2x/dt2) = -kx
(http://en.wikipedia.org/wiki/Simple_harmonic_motion)
That formula is derived from Newton's second law and Hooke's law. m is the inertial mass, x is the displacement from the equilibrium and k is the spring constant.
If m is the inertial mass, then is that the I in Faysal Riaz's experiment that he worked out using calculus?
If it is, then:
(Id²θ)/dt²= (-Mgθd²)/4y

∴(d²θ)/dt²= (-Mgθd²)/4Iy

I have worked out the rest of his work, and got to the part where I justify my hypothesis:
“It was hypothesised that the period will decrease as the horizontal distance between the strings increases in the form T is proportional to the inverse of D, and the period will also decrease as the vertical length of the strings increases in the form T is proportional to L, provided that the angle of amplitude, length of the ruler, and the mass of the ruler and strings are kept constant.”
By getting T \alpha 1/d (which Faysal had worked out already) and T\alpha\sqrt{y} (which was obtained from the same formula that T \alpha 1/d was obtained).
If this is not enough justification, we know that g is 9.8. Using this, it is possible to isolate g and have it equal:
g = (4pi²L²y)/3k²
And use the values obtained from the experiment to get a value for g. If it is close to 9.8, then the formula and results are justified (I have already done this and the answer was very close, so I know this formula is justified, along with my results)